[itachi-san]

There is an island upon which a tribe of blind people resides. They all answer devoutly to their chief. The tribe consists of 1000 people total, with 2 different eye colors. One day a miracle happened and every member (all 1000) was able to see for the first time. Without saying one word to each other they assembled in a congregation and their chief made the following rule: "Our religion forbids you to know your own eye color, or even to discuss the topic". Therefore, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his or her own (there are no reflective surfaces in any way shape or form for this puzzle). If a member does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and devout.

Of the 1000 islanders, it turns out that 100 of them have blue eyes and 900 of them have brown eyes. None of them know this at first of course, because any one member can only see the other 999 eye colors. What happens to the tribe, if anything, and why?

[akaslickster]

There is an island upon which a tribe of blind people resides. They all answer devoutly to their chief. The tribe consists of 1000 people total, with 2 different eye colors. One day a miracle happened and every member (all 1000) was able to see for the first time. Without saying one word to each other they assembled in a congregation and their chief made the following rule: "Our religion forbids you to know your own eye color, or even to discuss the topic". Therefore, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his or her own (there are no reflective surfaces in any way shape or form for this puzzle). If a member does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and devout.

Of the 1000 islanders, it turns out that 100 of them have blue eyes and 900 of them have brown eyes. None of them know this at first of course, because any one member can only see the other 999 eye colors. What happens to the tribe, if anything, and why?

all are blind therefore no suicides. Nothing happened.

[Guest]

This sounds very similar to this one.

where it triggers the chain like "someone lets it slip that there is at least 1 person with blue eyes" or something. This would cause the blue eyed ones to commit suicide on the 101th day, and the brown ones on the 102nd (I think).

Edited because I realized it was noon the next day, not the same.

Edited April 16, 2008 by imtcb

[bonanova]

There is a similarity, but let's see this one play out.

Clarification - "following day" means the day which follows a day in which

someone discovers [and I guess then must disclose] his/her own eye color?

[As opposed to the day that follows the day that everyone receives their sight.]

[akaslickster]

the miracle never happened because there was nothing or no one to create it in the first place. No genoside either.

[bonanova]

akaslickster,

The OP says

One day a miracle happened and every member (all 1000) was able to see for the first time.

Take that as a given.

Solve the puzzle as it's presented.

Try to find a solution that does not contradict the terms of the OP.

[Guest]

akaslickster,
The OP says
Take that as a given.
Solve the puzzle as it's presented.
Try to find a solution that does not contradict the terms of the OP.

Stab @ it- As most individuals would notice the difference in eye color, it stands to reason that at least one person would deduce their eye color eventually ( ie: they understand the 100/900 ratio later). Thus the eventual demise of the Islander population through suicide- given that all are devout & logical. BUT- This may not happen if a logical person understands these consequences, stands in the "river of denial" to save his own life, and refuses to accept the truth (honest-not a choice) or just doesn't care one way or the other.

[Guest]

900 brown eyed people commit suicide the 100 blue eyed do not.

the brown eyed people will see their own darker colored eyes in the blue-eyed people where as the opposite does not apply. therefore, the browneyed people will see that they actually have brown eyes

[itachi-san]

Stab @ it- As most individuals would notice the difference in eye color, it stands to reason that at least one person would deduce their eye color eventually ( ie: they understand the 100/900 ratio later). Thus the eventual demise of the Islander population through suicide- given that all are devout & logical. BUT- This may not happen if a logical person understands these consequences, stands in the "river of denial" to save his own life, and refuses to accept the truth (honest-not a choice) or just doesn't care one way or the other.

There is no denial. The OP states they are all highly devout.

[itachi-san]

900 brown eyed people commit suicide the 100 blue eyed do not.

the brown eyed people will see their own darker colored eyes in the blue-eyed people where as the opposite does not apply. therefore, the browneyed people will see that they actually have brown eyes

The OP states 'no reflective surfaces in any way shape or form'. In other words, the answer cannot involve reflections.

[Guest]

There is an island upon which a tribe of blind people resides. They all answer devoutly to their chief. The tribe consists of 1000 people total, with 2 different eye colors. One day a miracle happened and every member (all 1000) was able to see for the first time. Without saying one word to each other they assembled in a congregation and their chief made the following rule: "Our religion forbids you to know your own eye color, or even to discuss the topic". Therefore, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his or her own (there are no reflective surfaces in any way shape or form for this puzzle). If a member does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and devout.

Of the 1000 islanders, it turns out that 100 of them have blue eyes and 900 of them have brown eyes. None of them know this at first of course, because any one member can only see the other 999 eye colors. What happens to the tribe, if anything, and why?

1) they kill the chief for discussing the topic, loose on the discussion bit

2) Tomorrow never comes and their will be no suicide, therefore it does not matter if they know?

3) If they are logical - then they will realise that eye colour is unimportant in the great sceme of things and thus will consider the chief a bit of a crank, and ellect a new one democratically of course.

(Sounds like a paradox if they are logical and devout, except segregation by eye colour is a bit OTT)

[Guest]

Nothing happens to the tribe, everyone sees the other 999 eyes till they miraculously become blind again

[Brandonb]

There is an island upon which a tribe of blind people resides. They all answer devoutly to their chief. The tribe consists of 1000 people total, with 2 different eye colors. One day a miracle happened and every member (all 1000) was able to see for the first time. Without saying one word to each other they assembled in a congregation and their chief made the following rule: "Our religion forbids you to know your own eye color, or even to discuss the topic". Therefore, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his or her own (there are no reflective surfaces in any way shape or form for this puzzle). If a member does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and devout.

Of the 1000 islanders, it turns out that 100 of them have blue eyes and 900 of them have brown eyes. None of them know this at first of course, because any one member can only see the other 999 eye colors. What happens to the tribe, if anything, and why?

(I don't recall if eye color is dominant/recessive, or whatever)

When the a couple in the tribe (one partner having blue eyes, and one partner having brown eyes) has a child... If a parent sees that the child has a different eye color than his/her partner, than that parent will know their eye color is the same as the child, and will then kill themselves. In turn, when that parent kill him/herself, the other parent will kill themselves because they will know their eye color was different from the spouse when using the same reasoning. THEN when the child becomes so logical, if they possess the knowledge of their parents eye colors and the order of their deaths, then the child will know his/her own eye color and kill themselves. (though it is unlikely that they would recall their parents' eye colors from birth). So the parents (with different eye colors) of all the children would begin to die after the first child and leave their children behind. This would create a system of "have a child and there's a chance that you're gonna die)

Though again, this may not work because I don't know about the dominant/recessive stuff, though in that case the same would occur, but only if the baby was double recessive.

Edited April 16, 2008 by Brandonb

[Brandonb]

MORE for "Good Possibility"

THEN, using the same logic, if a partner does not commit suicide the next day, then both know they have the same eye color, and both kill themselves the next day (again leaving their child helpless because it cannot kill itself, nor know the rules). AND all people who already have children, no matter the age, follow the same reasoning and kill themselves, followed by their children who are able.

THEREFORE eliminating the population.

[Guest]

All the blue eyed people commit suicide on day 101 and all the brown eyed commit suicide on day 102?

Reasoning:

Each blue eyed person sees 99 other blue eyed people. Each of those people could deduce that, if they had brown eyes, then all the blue eyed people would see only 98 other blue eyed people. If they had only seen 98 other people, then they should all commit suicide on day 100 (see bottom paragraph below). As they don't commit suicide, he knows that they must see more than 98 and the only way this is possible is if he is himself blue. Each of the 100 apply the same logic, so commit suicide the following day (on day 101).

Meanwhile, all of the brown eyed people could see 100 blue eyes and 899 brown eyes. They know they could be blue or brown, but when all the blue eyed people commit suicide on day 101, they know that they are brown, so they commit suicide the following day on day 102.

If the first paragraph doesn't immediately make sense, reduce it down to 1 and work up. e.g. If there was only 1 blue eyed person, he would see all brown eyes and commit suicide the next day (day 2). (This is because they all know that there are 2 eye colours on the island so this person knows that they must be the odd one out). If there were two blue eyed people, because they could see another pair of blue eyes they wouldn't commit suicide the next day (thinking it might be just the other guy). Because neither commit suicide the next day they know that they each saw another pair of blue eyes and they know that this is only possible if they were each blue eyes, so they both commit suicide the following day (day 3). This reasoning carries all the way up to 100.

[Brandonb]

All the blue eyed people commit suicide on day 101 and all the brown eyed commit suicide on day 102?

Reasoning:

Each blue eyed person sees 99 other blue eyed people. Each of those people could deduce that, if they had brown eyes, then all the blue eyed people would see only 98 other blue eyed people. If they had only seen 98 other people, then they should all commit suicide on day 100 (see bottom paragraph below). As they don't commit suicide, he knows that they must see more than 98 and the only way this is possible is if he is himself blue. Each of the 100 apply the same logic, so commit suicide the following day (on day 101).

Meanwhile, all of the brown eyed people could see 100 blue eyes and 899 brown eyes. They know they could be blue or brown, but when all the blue eyed people commit suicide on day 101, they know that they are brown, so they commit suicide the following day on day 102.

If the first paragraph doesn't immediately make sense, reduce it down to 1 and work up. e.g. If there was only 1 blue eyed person, he would see all brown eyes and commit suicide the next day (day 2). (This is because they all know that there are 2 eye colours on the island so this person knows that they must be the odd one out). If there were two blue eyed people, because they could see another pair of blue eyes they wouldn't commit suicide the next day (thinking it might be just the other guy). Because neither commit suicide the next day they know that they each saw another pair of blue eyes and they know that this is only possible if they were each blue eyes, so they both commit suicide the following day (day 3). This reasoning carries all the way up to 100.

I'm pretty sure that line of reasoning ends at 4 blue eyed people. I may be wrong, but as long as a blue eyed person (who doesn't know it) sees 3 other blue eyed people, then their is no logic to lead on to kill him/herself.

[Guest]

I think none of the islanders will kill themselves, and here's why:-

We (the puzzler) know from the OP that there is 100 Blue and 900 brown, but is not suggested in the original puzzle that the islanders know this, so the blue eyed people see 99 people with blue eyes and 900 people with with brown eyes and the brown eyed people see 100 people with blue eyes and 899 people with brown eyes. However as they are not allowed to discuss this it can not affect them at all. In fact all would suspect that they have brown eyes as there is a 9 in 10 chance of this but certainly no racing certainty.

Or.....

If the islanders know that there is the 100 / 900 split then on day 2 (ie the following day) all would kill themselves, because as mentioned above the blue eyed people see 99 people with blue eyes and 900 people with with brown eyes and the brown eyed people see 100 people with blue eyes and 899 people with brown eyes. and then this becomes not so much as a logic problem as a straight out math problem (blues eyes calculate I only see 99 blue i'm the other one. Brown eyes calculate I see all blue eyes therefore I'm brown)

[akaslickster]

I did some searching and found it in a yahoo riddle file using some different words like red eyes. Same type of situation good luck everyone. Im no spoiler

[Guest]

I'm pretty sure that line of reasoning ends at 4 blue eyed people. I may be wrong, but as long as a blue eyed person (who doesn't know it) sees 3 other blue eyed people, then their is no logic to lead on to kill him/herself.

It should be relatively straightforward induction...

From my previous reasoning we have if there is 1 person with blue eyes, he will kill himself on day 2, and if there are 2 people with blue eyes they will kill themselves on day 3.

Now, if there's 3, each person may think there may be only 2. As previously proven, if there are 2, then they will kill themselves on day 3, so if no one kills themselves on day 3 there must be more than 2. If no one else has blue eyes the only way that can be possible is if you have blue eyes. All 3 apply the same logic, so all 3 people kill themselves on day 4.

Let's cut and paste that a couple of times, just changing the numbers...

Now, if there's 4, each person may think there may be only 3. As previously proven, if there are 3, then they will kill themselves on day 4, so if no one kills themselves on day 4 there must be more than 3. If no one else has blue eyes the only way that can be possible is if you have blue eyes. All 4 apply the same logic, so all 4 people kill themselves on day 5.

...

Now, if there's n, each person may think there may be only n-1. As previously proven, if there are n-1, then they will kill themselves on day n, so if no one kills themselves on day n there must be more than n-1. If no one else has blue eyes the only way that can be possible is if you have blue eyes. All n apply the same logic, so all n people kill themselves on day n+1.

This goes on until the smaller group kill themselves, because as soon as one group kills themselves, everyone else must know they belong to the other group and so will kill themselves the next day.

Of course, the OP only says that they are all highly logical and devout, which is a good proof that this does not mean intelligent. If they were in any way intelligent, they would immediately oust the chief for attempted mass murder and appoint a new chief who wouldn't try to kill them all!

[unreality]

this is like Josephine, but with one major difference

nobody dies, because they don't know what we know. They don't know the 900-100 split numbers. In Josephine riddle, all the wives with cheating husbands shoot their husbands on the 40th day because there's the 'at least one' to kick it off. Obviously there's at least one of both eye colors- each person sees either 99 blue and 900 brown or 100 blue and 899 brown. But they don't know what there's SUPPOSED to be, so there's no ladder that leads up to mass suicide on days 101/102

[itachi-san]

this is like Josephine, but with one major difference

nobody dies, because they don't know what we know. They don't know the 900-100 split numbers. In Josephine riddle, all the wives with cheating husbands shoot their husbands on the 40th day because there's the 'at least one' to kick it off. Obviously there's at least one of both eye colors- each person sees either 99 blue and 900 brown or 100 blue and 899 brown. But they don't know what there's SUPPOSED to be, so there's no ladder that leads up to mass suicide on days 101/102

Perhaps the chief isn't as evil as previous posts have made him out to be

[Brandonb]

Perhaps the chief isn't as evil as previous posts have made him out to be

But what about the children?

[Guest]

this is like Josephine, but with one major difference

nobody dies, because they don't know what we know. They don't know the 900-100 split numbers. In Josephine riddle, all the wives with cheating husbands shoot their husbands on the 40th day because there's the 'at least one' to kick it off. Obviously there's at least one of both eye colors- each person sees either 99 blue and 900 brown or 100 blue and 899 brown. But they don't know what there's SUPPOSED to be, so there's no ladder that leads up to mass suicide on days 101/102

Exactly what I said in post #3. I couldn't find the trigger because there isn't one. I said that if there was such a trigger it would be days 101 for the blue and 102 for the brown.

[Guest]

whoa what is the question here? what are u askin for?

[itachi-san]

whoa what is the question here? what are u askin for?

Can you please stop cutting and pasting this silly post? Read the OP, then ask a specific question.

[Guest]

Do the people of the tribe know that 900 people have brown eyes and 100 people have blue?